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A073600 Least n^k with same leading decimal digit as n, k>1. 3
1, 256, 387420489, 4096, 59604644775390625, 60466176, 79792266297612001, 8589934592, 984770902183611232881, 100, 121, 144, 169, 196, 11390625, 1048576, 1419857, 104976, 130321, 25600000000, 278218429446951548637196401 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
a(n) = n^A073601(n);
A000030(a(n)) = A000030(n).
EXAMPLE
a(4)=4096, as 4096=4^6 is the least power of 4 with initial digit =4: 4^2=16, 4^3=64, 4^4=256 and 4^5=1024; A073601(4)=6.
MAPLE
f:= proc(n) local t, k, m;
t:= floor(n/10^ilog10(n));
for k from 2 do
m:= n^k;
if floor(m/10^ilog10(m)) = t then return m fi
od
end proc:
map(f, [$1..100]); # Robert Israel, Apr 21 2021
MATHEMATICA
fi[n_] := First[IntegerDigits[n]]; Table[k = 2; While[fi[x = n^k] != fi[n], k++]; x, {n, 21}] (* Jayanta Basu, Jul 02 2013 *)
CROSSREFS
Sequence in context: A017096 A017192 A013879 * A070327 A008972 A017300
KEYWORD
nonn,base,look
AUTHOR
Reinhard Zumkeller, Aug 04 2002
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)